My betta has a piece of algae stuck in his left gill and he won't come up from the bottom of his tank.

I can see it's bothering him and he's looking at it breathing hard like he's trying to get it out.I think he's struggling to get oxygen. I managed to dislodge some of it with the non-ink end of a pen, but I don't know how to get the rest out without hurting him. My sister suggested using tweezers. but I don't know if that's safe.... is it?